JPH0422456B2 - - Google Patents

Description

[Detailed description of the invention]

[Industrial Application Field] The present invention relates to a method for diagnosing abnormal conditions in rotating machines such as reducers, motors, and blowers, or rotating machine elements such as bearings and gears. [Prior Art] In rotating machines such as motors and blowers, or rotating machine elements such as rolling bearings and gears, wear and damage due to rotation, damage due to poor lubrication, and damage due to poor assembly occur. For this reason,
It becomes necessary to detect and deal with damage caused to rotating machinery and the like at an early stage. Diagnostic methods for abnormalities in rotating machinery include wear,
Vibration methods that capture vibrations caused by abnormalities such as damage are common. Conventional vibration methods measure the vibrations of rotating machinery, etc., and perform fast Fourier transform on the vibrations to convert the vibrations, which are irregular functions expressed in the time domain, into functions in the frequency domain, and calculate their power spectrum. was determined, and a deterioration index was calculated from the determined power spectrum to determine abnormal conditions in rotating machinery, etc. [Problem to be solved by the invention] Vibrations in rotating machines, etc. include vibrations (noise) other than vibrations caused by abnormalities such as wear and damage, especially transient ones, so conventional vibrations The method could not completely remove these noises, and an accurate deterioration index could not be calculated. Furthermore, it is not possible to accurately calculate the deterioration index even when the spectra of interest are close to each other. [Means for solving the problem] The present invention has been made in view of the above circumstances, and can remove vibrations (noise) other than vibrations caused by abnormalities, and can calculate accurate deterioration index. The purpose is to provide a diagnostic method for rotating machinery. The present invention measures vibrations in a rotating machine, calculates a power spectrum by applying an autoregressive model to the measured signal to remove transient noise, and calculates the intensity at a specific frequency of this power spectrum and the effective value of the power spectrum. The ratio of is calculated as the deterioration index,
The method is characterized in that a deterioration probability is calculated from the calculated deterioration index. [Principle] The principle of the method of the present invention will be explained below. FIG. 1 shows a detection signal of vibration in a rotating machine. Now, if the magnitude of vibration at time t is _xt , it is considered that vibrations due to various factors are superimposed on this signal. Therefore, considering this signal as a superimposed signal of various vibrations, an autoregressive equation shown in equation (1) is set. x _t = a ₁ α ₁ + a ₂ α ₂ +…u _t = _M 〓 ⁱ⁼¹ a _i α _i +u _t …(1) a _i : System parameter α _i : Quantized vibration in the vibration at time t Component u _t : White noise (a random signal having a constant power spectral density independent of frequency) M : System order Here, consider the system parameters and system order. First, when the system order M=1, equation (1) can be expressed as follows. x _t = a ₁ α ₁ + u _t ……(2) In equation (2), if x _t is known (measured value), then u _t = x _t −a ₁ α ₁ ……(2)′, and a ₁ If α ₁ is considered as an estimated value, u _t represents the error. Therefore, the optimum value of a ₁ is determined by the method of least squares. In other words, the value of a ₁ that minimizes the expected value E[u _t ² ] of u _t ² is the optimal value. Then, based on the obtained value _a1 , the expected value E[u _t ]M=1 of ut is calculated. Next, considering the case where the system order M=2, equation (1) becomes x _t =a ₁ α ₁ +a ₂ α ₂ + _ut (3). Here, a ₁ obtained by the above least squares method
Substituting the value of a ₂
The expected value E[ _ut ] _M=2 of u _t is calculated based on the obtained values a ₁ and a ₂ . Then, the previously obtained expected value E[u _t ] _M = 1 of u _t and this E[u _t ] _{M = 2} are compared. Below, use the same procedure to find the expected value E [u _t ] _M=i , and
Let i be the system order M when the difference between [u _t ] _M=i-1 and E[u _t ] _M=i becomes a predetermined minimum value or less.
In other words, a ₁ α ₁ , a ₂ α ₂ , . . . , a _M α _M are considered to be vibration components with different causes, and if these vibration components are minute and are less than a predetermined value, they are treated as white noise. Therefore, x _t expressed by a predetermined order M is considered to be a value representing the vibration from which noise is removed at time t. A similar method is used to remove noise from vibration signals extracted at predetermined time intervals. Based on the vibration signal obtained in this way from which noise has been removed, its power spectrum is determined. The power spectrum is expressed by the following equation (4). However, f: Frequency σu ² : Variance of statistical estimation The power spectrum can be obtained from equation (4), but
If there is an abnormality in a rotating machine or the like, the intensity of the power spectrum will partially increase due to the abnormality.
Therefore, if the intensity of the power spectrum is partially large, it can be inferred that an abnormality has occurred in a rotating machine, etc., but depending on the type of rotating machine, etc. or the type of abnormality, it can be assumed that the cause is due to an abnormality. The frequency characteristics of the prominent state of the power spectrum intensity are different. Therefore, as a deterioration index representing the degree of abnormality in a rotating machine, the ratio between the effective value of the power spectrum intensity in the entire frequency range and the power spectrum intensity at the characteristic frequency defined by each abnormality is used. FIG. 2 A to E show the relationship between the power spectrum intensity and the characteristic frequency caused by each abnormality in the rotating machine. Figure 2A shows the state in which the rotating shaft of a rotating machine is unbalanced, and fo indicates the frequency of the rotating shaft. The deterioration index F ₁ in this case is F ₁ =S ₁ /Srms (5) where, S ₁ : power spectrum intensity at frequency fo Srms : expressed as an effective value in the entire frequency range of the power spectrum. Figure 2 (b) shows a state in which misalignment or bent shaft occurs in a rotating machine, and the deterioration index F ₂ is F ₂ =√S ₂ ² + S ₃ ² /Srms ……(6) S ₂ , S ₃ : Frequency It is expressed as the power spectrum intensity at 2fo and 3fo. FIG. 2C shows a case where there is play in the rotating machine, and _the deterioration index _{F 3} is expressed by the power spectrum intensity at frequency 1 _/ 2fo. FIG. 2D shows a case where an abnormality has occurred in the bearing. In a bearing, the outer ring, inner ring, and rolling elements each have a power spectrum intensity as shown in FIG. 2D, but the frequency characteristics of each are different. K _i (i=1 to 3) in the figure is the outer ring, the inner ring,
It is a constant corresponding to each part when there is an abnormality in any of the rolling elements, K ₁ is the outer ring abnormality,
K ₂ shows the inner ring abnormality, and K ₃ shows the rolling element abnormality. K ₁ , K ₂ , and K ₃ are expressed as follows. K ₁ =n/2(1-d/Dcosα) ……(7) K ₂ =n/2(1+d/Dcosα) ……(8) K ₃ =D/d{1-(d/D) ² cosα } ...(9) However, n: Number of rolling elements d: Diameter of the rolling element D: Diameter of pitch circle of the rolling element α: Contact angle of the rolling element Each deterioration index of the outer ring, inner ring, and rolling element is as follows. is expressed in F _4i =√S ₁ ² +S ₂ ² +S ₃ ² /Srms...(10) F ₄₁ : Outer ring deterioration index F ₄₂ : Inner ring deterioration index F ₄₃ : Rolling element deterioration index S ₁ , S ₂ , S ₃ :Frequency Kifo (i= ₁ , ₂ , ₃ )2Kifo,
3 Power spectrum intensity in Kifo Figure 2 E shows the relationship between the power spectrum intensity and characteristic frequency when the gear is in a deteriorated state, where f _G is the meshing frequency of the gear, and f _G = Z・fo......(11) Z : Number of teeth fo: Number of rotations of the shaft. Then, the deterioration index F ₅ of this gear is F ₅ =√S ₁ ² + S ₂ ² /Srms ... (12) S ₁ , S ₂ : Each power spectrum intensity at frequency f _G , 2f _G This deterioration index causes abnormality. The state is recognized, but the probability of deterioration is determined to further evaluate the degree of abnormality. In general, in reliability theory, the random failure probability R(t) is determined as R(t) = 1-e ^- 〓 ^t ...(13) and is said to follow an exponential distribution, and the deterioration probability is determined by the deterioration index F. Below as a function (14)
It is expressed by the formula. In other words, if the probability of deterioration is P(F) and the deterioration index is F, then However, Lo: Maximum value of deterioration index when no abnormality is considered to occur {P(F)=0} Mo: Maximum value of deterioration index during life {P(F)=1.0} Xo: Deterioration probability The deterioration index nx when it becomes 0.5 is the slope of the exponential curve (determined by the type of abnormality, etc.). When equation (14) is expressed graphically, it becomes a curve as shown in FIG. Through basic experiments and confirmatory tests of field data, the inventor of the present application has obtained the results shown in FIG.
Deterioration probability curves were obtained for each rotary machine or the deterioration index for various abnormalities in the rotary machine, etc., obtained using equations (5) to (12). This is shown in Figures 4-8. Figure 4 shows the relationship between the deterioration index and the deterioration probability when the rotation axis is unbalanced.
The figure shows the relationship between the deterioration index and the probability of deterioration when the rotating machine is in a misalignment or bent shaft state, and Figure 6 shows the relationship between the deterioration index and the probability of deterioration when there is play in the rotating machine. ing. Figures 7A to 7C show cases where an abnormality occurs in the bearing. Figure 7A shows a case where an abnormality occurs in the outer ring of the bearing, and Figure 7B shows a case where an abnormality occurs in the inner ring of the bearing. Figure 7C shows the deterioration probability relative to the deterioration index when an abnormality occurs in the rolling elements of the bearing. FIG. 8 shows the deterioration probability relative to the deterioration index when an abnormality occurs in the gear. Therefore, when the deterioration index is determined using the above equations (5) to (12), the deterioration probability is determined from the graphs shown in FIGS. 4 to 8, and the specific degree of abnormality in each rotating machine can be grasped. [Example] FIG. 9 is a schematic block diagram of an apparatus used to carry out the method of the present invention. In the figure, 1 is a motor, and the output shaft of the motor 1 is connected to a shaft 5 through a coupling 2. The shaft 5 is rotatably supported at both ends by bearings 3, 3, respectively.
A load is applied to the hydraulic cylinder 6. A vibration pickup 7 is attached to one of the bearings 3, which captures vibrations of the bearing 3 and outputs a predetermined signal to a vibration meter 8. The output of the vibrometer 8 is given to the arithmetic processing section 10 via the A/D converter 9, and the arithmetic processing section 10, as mentioned above, performs vibrations at predetermined intervals based on the output of the A/D converter 9. The vibration of the bearing 3 is extracted, the vibration at each time is quantized, and noise superimposed on the vibration is removed. Then, a power spectrum is calculated based on the vibration from which noise has been removed at each time, and each deterioration index is calculated. Furthermore, the deterioration probability is calculated from the relationship between the preset deterioration index and the deterioration probability. Arithmetic processing unit 1
The calculation result of 0 is displayed and printed on the display/print section 11. FIG. 10 shows a power spectrum obtained by an autoregressive model when a normal bearing is diagnosed using this device. Moreover, FIG. 11 shows a power spectrum obtained by an autoregressive model of a bearing with an artificial defect added to the outer ring. Furthermore, Table 1 shows the deterioration index of each bearing, normal and abnormal, and the deterioration probability determined from the deterioration index. As is clear from Table 1, the probability of deterioration of the outer ring is 100%, and it becomes clear that an abnormality has occurred in the outer ring. Note that FIG. 12 shows the results of fast Fourier transform of the vibrations of a normal bearing, and FIG. 13 shows the results of fast Fourier transform of the vibrations of a bearing with an artificial defect on the outer ring.

〔effect〕

According to the present invention, the type and degree of abnormality in a rotating machine can be clearly grasped without being affected by noise, etc., and the rotating machine, etc. can be diagnosed with high accuracy.

[Brief explanation of drawings]

Fig. 1 is a graph for explaining the method of the present invention, Fig. 2 I to E are graphs for explaining the deterioration index calculation method, and Figs. 3 to 8 show the relationship between the deterioration index and the probability of deterioration. Graphs, FIG. 9 is a schematic block diagram of the apparatus used to carry out the method of the present invention, FIGS. 10 and 11 are graphs showing autoregressive modeling of bearing vibration in the method of the present invention, and FIGS. 12 and 13. The diagram is
It is a graph obtained by fast Fourier transform of bearing vibration using a conventional method. 1...Motor, 2...Coupling, 3...Bearing, 5...Shaft, 7...Vibration pick-up.

Claims (1)

[Claims] 1. Measure the vibration in a rotating machine, create a power spectrum by modeling the measured signal into an autoregressive model to remove transient noise, and calculate the ratio of the intensity at a specific frequency of this power spectrum to the effective value of the power spectrum. A method for diagnosing a rotating machine, characterized by calculating a deterioration index and calculating a deterioration probability from the calculated deterioration index.